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A perturbative analysis of modulated amplitude waves in Bose-Einstein condensates
Mason A Porter1, Predrag Cvitanović
1School of Mathematics and Center for Nonlinear Science, Georgia Institute of Technology, Atlanta, Georgia 30332, USA. mason@math.gatech.edu
Chaos (Woodbury, N.Y.)
|September 28, 2004
Abstract:
We apply Lindstedt's method and multiple scale perturbation theory to analyze spatio-temporal structures in nonlinear Schrödinger equations and thereby study the dynamics of quasi-one-dimensional Bose-Einstein condensates with mean-field interactions. We determine the dependence of the amplitude of modulated amplitude waves on their wave number. We also explore the band structure of Bose-Einstein condensates in detail using Hamiltonian perturbation theory and supporting numerical simulations.